MinT - Best Known (90−54, 90, s)-Nets in Base 32

Best Known (90−54, 90, s)-Nets in Base 32

(90−54, 90, 142)-Net over F₃₂ — Constructive and digital

Digital (36, 90, 142)-net over F₃₂, using

2 times m-reduction [i] based on digital (36, 92, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 29, 44)-net over F₃₂, using
    - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
  2. digital (7, 63, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(90−54, 90, 273)-Net over F₃₂ — Digital

Digital (36, 90, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 90, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(90−54, 90, 288)-Net in Base 32 — Constructive

(36, 90, 288)-net in base 32, using

t-expansion [i] based on (35, 90, 288)-net in base 32, using
- 1 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
  - base change [i] based on digital (9, 65, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(90−54, 90, 342)-Net in Base 32

(36, 90, 342)-net in base 32, using

6 times m-reduction [i] based on (36, 96, 342)-net in base 32, using
- base change [i] based on digital (20, 80, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(90−54, 90, 36647)-Net in Base 32 — Upper bound on s

There is no (36, 90, 36648)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2907 886420 920799 949272 063090 162175 459629 480728 530807 708890 522309 893770 625244 874963 598166 453266 858191 644491 849542 178927 535843 686579 538596 > 32⁹⁰ [i]